Average Error: 0.2 → 0.3
Time: 6.8s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot y\right) \cdot 3\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot y\right) \cdot 3
double f(double x, double y) {
        double r745084 = x;
        double r745085 = 16.0;
        double r745086 = 116.0;
        double r745087 = r745085 / r745086;
        double r745088 = r745084 - r745087;
        double r745089 = 3.0;
        double r745090 = r745088 * r745089;
        double r745091 = y;
        double r745092 = r745090 * r745091;
        return r745092;
}
↓
double f(double x, double y) {
        double r745093 = x;
        double r745094 = 16.0;
        double r745095 = 116.0;
        double r745096 = r745094 / r745095;
        double r745097 = r745093 - r745096;
        double r745098 = y;
        double r745099 = r745097 * r745098;
        double r745100 = 3.0;
        double r745101 = r745099 * r745100;
        return r745101;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)}\]

  4. Simplified0.3

    \[\leadsto \left(x - \frac{16}{116}\right) \cdot \color{blue}{\left(y \cdot 3\right)}\]
  5. Using strategy rm

  6. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(x - \frac{16}{116}\right) \cdot y\right) \cdot 3}\]

  7. Final simplification0.3

    \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot y\right) \cdot 3\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))